Consider combinations of three factors in the removal of dirt from standard loads of laundry. The first factor is the brand of the detergent, X, Y , or Z. The second factor is the type of detergent, liquid or powder. The third factor is the temperature of the water, hot or warm. The experiment was replicated three times. Response is percent dirt removal. The data are as follows:

(a) Are there significant interaction effects at the α = 0.05 level?
(b) Are there significant differences between the three brands of detergent?
(c) Which combination of factors would you prefer to use?

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Brand Type Temperature х Powder Hot Warm 85 88 80 82 83 85 78 75 72 Liquid Hot Warm 75 75 73 Powder Hot 90 92 92 Warm 88 86 88 Liquid Hot 78 76 70 Warm 76 77 76 Powder Hot 85 87 88 Warm 76 74 78 Liquid Hot 60 70 68 Warm 55 57 54